a movie theater charges $9.00 for adults and $7.00 for children. On a day when 325 people purchased tickets, the total receipts were $2675. How many adults tickets were sold? How many children tickets were sold? Create a system of linear equations and solve it using matrices.

johnny23o wrote:a movie theater charges $9.00 for adults and $7.00 for children. On a day when 325 people purchased tickets, the total receipts were $2675. How many adults tickets were sold? How many children tickets were sold? Create a system of linear equations and solve it using matrices.

Your problem states that people attended the theater that day, grossing , at per ticket per adult ()and per ticket per child (). This means that times , the number of adults, plus times , the number of children, produced , and that the total number of adults, , plus children, , was . This is your system of linear equations:

You mentioned that you needed to use matrices to solve the problem. Then you will need to convert your system of linear equations to matrix form, as follows:

This will produce a matrix equation of the form for:

such that:

Given and , you need to find , the inverse matrix of , if it exists, to solve the equation. Using elementary row operations on , the augmented matrix of , allows you to obtain :